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Mathematics > Rings and Algebras

arXiv:0710.2748 (math)
[Submitted on 15 Oct 2007 (v1), last revised 18 Nov 2008 (this version, v2)]

Title:Algebraic curves for commuting elements in the q-deformed Heisenberg algebra

Authors:Marcel de Jeu, Christian Svensson, Sergei Silvestrov
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Abstract: In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series.
Comments: 18 pages, 2 figures, LaTeX. Final version with some improvements in presentation. To appear in Journal of Algebra.
Subjects: Rings and Algebras (math.RA); Quantum Algebra (math.QA)
MSC classes: 16S99 (Primary) 81S05, 39A13 (Secondary)
Report number: MI 2007-21
Cite as: arXiv:0710.2748 [math.RA]
  (or arXiv:0710.2748v2 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.0710.2748
Journal reference: Journal of Algebra 321 (2009), pp. 1239-1255
Related DOI: https://doi.org/10.1016/j.jalgebra.2008.10.021

Submission history

From: Marcel de Jeu [view email]
[v1] Mon, 15 Oct 2007 09:13:20 UTC (18 KB)
[v2] Tue, 18 Nov 2008 13:15:01 UTC (19 KB)
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